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Geometry problem...

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hey guys I''ve got a math problem... I''ve got a circle and an ellipse. I know the radius of the circle, and the height of the ellipse. What I want to figure out is the width of the ellipse. I want it wide enough so that when the top of the ellipse touches the top of the circle, it just barely completely encloses the circle. You know? So I guess that means it goes through the right and left side of the sphere (that way it encloses it completely), right? But I can''t figure out the rest.... which is where you hopefully come in? I swear this isn''t homework, I need it for a game Any help appreciated.

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